Display processing method and apparatus

ABSTRACT

A disclosed method includes: identifying an axis that is a straight or curved line inside of a space; first generating plural surface regions that are orthogonal to the identified axis; second generating, from a first vector provided at each vertex of an unstructured grid disposed inside of the space, a second vector at each point of plural points on a surface region for each of the generated plural surface regions; and displaying an arrow corresponding to the generated second vector.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority of theprior Japanese Patent Application No. 2012-158754, filed on Jul. 17,2012, the entire contents of which are incorporated herein by reference.

FIELD

This invention relates to a display processing method and apparatus.

BACKGROUND

Along with the enhancement of the processing ability of the computer, anumerical analysis of a fluid inside of various objects is conducted.For example, the numerical analysis for reproducing a function of aheart is performed with respect to a blood flow inside of the heart.

Conventionally, in such a numerical analysis, the blood flow isdisplayed using following methods:

(A) Vector Display

Blood flow vectors obtained by the numerical analysis are displayed asarrows as they are.

(B) Particle Flow

Plural particles having no weight are inputted from an arbitraryposition in a vector field. Movement direction and amount of eachparticle are calculated depending on either of the steady-state analysisand non-steady-state analysis. In other words, the particles are movedin sequence to display the flow.

When the blood flow inside of the heart is simply displayed, displays asillustrated in FIGS. 1 and 2 may be conducted. FIGS. 1 and 2 illustratethe blood flows in left and right ventricles in different angles.However, the vectors obtained by the numerical analysis are display asthey are, therefore, the states of the blood flows are unclear, becausea lot of arrows overlap.

RELATED ARTS Non-Patent Documents

-   [Non-Patent Document 1] “AVS Express Module reference”, CYBERNET    SYSTEMS CO., LTD., p. T-84, August 2010-   [Non-Patent Document 2] SCHROEDER WILL et al., “The visualization    toolkit”, 2nd edition, Prentice Hall PTR, ISBN 0-13-954694-4, pp.    200-203, 1997

SUMMARY

A display processing method relating to one mode of this inventionincludes: (A) identifying an axis that is a straight or curved lineinside of a space; (B) first generating plural surface regions that areorthogonal to the identified axis; (C) second generating, from a firstvector provided at each vertex of an unstructured grid disposed insideof the space, a second vector at each point of plural points on asurface region for each of the generated plural surface regions; and (D)displaying an arrow corresponding to the generated second vector.

The object and advantages of the embodiment will be realized andattained by means of the elements and combinations particularly pointedout in the claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and arenot restrictive of the embodiment, as claimed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram to explain a problem of a conventional art;

FIG. 2 is a diagram to explain the problem of the conventional art;

FIG. 3 is a functional block diagram of an information processingapparatus relating to an embodiment of this invention;

FIG. 4 is a diagram depicting a processing flow relating to thisembodiment;

FIG. 5 is a schematic diagram depicting a structure of a heart;

FIG. 6 is a diagram depicting an entire heart;

FIG. 7 is a diagram depicting an example of a first axis candidateidentified in the left ventricle;

FIG. 8 is a diagram depicting an example of a second axis candidateidentified in the left ventricle;

FIG. 9 is a diagram depicting an example of a third axis candidateidentified in the left ventricle;

FIG. 10 is a diagram depicting an example of a first axis candidateidentified in the right ventricle;

FIG. 11 is a diagram depicting an example of a second axis candidateidentified in the right ventricle;

FIG. 12 is a diagram depicting an example of a third axis candidateidentified in the right ventricle;

FIG. 13 is a diagram to explain a process to calculate a fourth axiscandidate identified in the right ventricle;

FIG. 14 is a diagram to explain the process to calculate the fourth axiscandidate identified in the right ventricle;

FIG. 15 is a diagram to explain the process to calculate the fourth axiscandidate identified in the right ventricle;

FIG. 16 is a diagram to explain the process to calculate the fourth axiscandidate identified in the right ventricle;

FIG. 17 is a diagram to explain the process to calculate the fourth axiscandidate identified in the right ventricle;

FIG. 18 is a diagram to explain the process to calculate the fourth axiscandidate identified in the right ventricle;

FIG. 19 is a diagram to explain a position of a surface region;

FIG. 20 is a diagram to explain lattice points on the surface region;

FIG. 21 is a diagram to explain a processing for calculating vectors atthe lattice points;

FIG. 22 is a diagram to explain the processing for calculating vectorsat the lattice points;

FIG. 23 is a diagram depicting a processing flow relating to thisembodiment;

FIG. 24 is a diagram to explain an effect of this embodiment;

FIG. 25 is a diagram depicting an effect of this embodiment;

FIG. 26 is a diagram depicting an example in which the right ventricleis displayed by the conventional art;

FIG. 27 is a diagram depicting an example in which the right ventricleis displayed by this embodiment; and

FIG. 28 is a functional block diagram of a computer.

DESCRIPTION OF EMBODIMENTS

In this embodiment, as one example, a case is presumed where results ofthe numerical analysis for the heart are displayed as vectors. However,this embodiment can be applied to a case where the results of thenumerical analysis for other objects are displayed as vectors.

FIG. 3 illustrates a configuration of an information processingapparatus 100 relating to this embodiment. The information processingapparatus 100 relating to this embodiment includes a first data storageunit 110, a vector display processing unit 120, a second data storageunit 130, an input unit 140 and a display unit 150. The vector displayprocessing unit 120 includes an axis processing unit 121, a planegenerator 122, a vector generator 123 and a rendering processing unit124.

The first data storage unit 110 stores, as results of the numericalanalysis, coordinates of each vertexes of each tetrahedral element,element information (e.g. attributes of the tetrahedral element (e.g.attribute representing whether the tetrahedral element belongs toportions of the heart such as the heart muscle or portion in which theblood flows.)), a physical value at each vertex (e.g. vectorrepresenting a velocity of the blood flow in case of the tetrahedralelements included in the portion in which the blood flows), and aphysical value in each tetrahedral element. Because the results of thenumerical analysis change with respect to time, the results of thenumerical analysis includes the results of the numerical analysis foreach time step.

The vector display processing unit 120 performs a vector displayprocessing for displaying a vector that is set at each vertex of thetetrahedral element as an arrow.

The axis processing unit 121 in the vector display processing unit 120performs a processing for identifying an axis to determine a surfaceregion that is used in a following processing in the right ventricle orleft ventricle in this embodiment. The plane generator 122 performs aprocessing for generating plural surface regions that intersectperpendicularly to the axis identified by the axis processing unit 121.The vector generator 123 generates a vector at each point on eachsurface region of the plural surface regions that are generated by theplane generator 122, from the vectors at each vertex of each tetrahedralelement. The second data storage unit 130 stores data such as axis,plane and vector. The rendering processing unit 124 performs aprocessing for rendering portions of the heart such as heart muscle andarrows each of which represents the vector generated for each surfaceregion, to display the objects onto the display unit 150. The input unit140 accepts input and selection data from a user.

Next, processing contents of the information processing apparatus 100will be explained by using FIGS. 4 to 27. The vector display processingunit 120 performs a display to prompt the user to select a displaytarget on the display unit 150, and input unit 140 accepts selection ofthe display target from the user (FIG. 4: step S1). In this embodiment,it is presumed that either of the right ventricle and left ventricle isselected. The input unit 140 outputs data of the selected display targetto the vector display processing unit 120. The vector display processingunit 120 accepts the data of the selected display target from the inputunit 140.

The structure of the heart is as illustrated in FIG. 5, for example. Theblood flows into the right ventricle from the tricuspid valve, and theblood flows out from the right ventricle through the pulmonary valve.Moreover, the blood flows into the left ventricle from the mitral valve,and the blood flows out from the left ventricle through the aorticvalve. The apex portion is identified as a reference point in a lowerportion of the heart. In addition to the apex portion, an apex portionof the right ventricle is also identified in the bottom inside of theright ventricle.

Then, the axis processing unit 121 calculates preset axis candidates forthe selected display target, and stores data of the axis candidates inthe second data storage unit 130 (step S3).

In this embodiment, when the left ventricle is selected as a displaytarget, three axis candidates are calculated. However, the axiscandidates may be set manually in advance, and stored in the second datastorage unit 130 or the like.

For example, the heart as illustrated in FIG. 6 has the left ventricleA, left atrium B, right ventricle C and right atrium D, and when payingattention to the left ventricle A, a line segment connecting a center aof gravity for a surface region including an annulus of the mitral valvewith the apex portion c as a first axis candidate is calculated asillustrated in FIG. 7. The surface region including the annulus of themitral valve or the center a of gravity for the surface region includingthe annulus of the mitral valve may be preset, or may be extracted fromits features. The apex portion c may be preset or may be extracted fromits features.

In addition, as illustrated in FIG. 8, a line segment connecting acenter b of gravity for a surface region including the annulus of theaortic valve with the apex portion c is calculated as the second axiscandidate. The annulus of the aortic valve or the center b of gravityfor the surface region including the annulus of the aortic valve may bepreset or may be extracted from its features.

Furthermore, as illustrated in FIG. 9, a line segment connecting amiddle point d between the center a of gravity for the surface regionincluding the annulus of the mitral valve and the center b of gravityfor the surface region including the annulus of the aortic valve withthe apex portion c is calculated as the third axis candidate.

Moreover, when the right ventricle C is selected as the display target,four axis candidates are calculated. However, the axis candidates may bepreset manually, and stored in the second data storage unit 130 or thelike.

For example, as illustrated in FIG. 10, a line segment connecting acenter e of gravity for a surface region including an annulus of thepulmonary valve with an apex portion h of the right ventricle iscalculated as the first axis candidate. The annulus of the pulmonaryvalve or the center e of gravity for the surface region including theannulus of the pulmonary valve may be preset, or may be extracted fromits features. The apex portion h of the right ventricle is a bottomportion of the right ventricle furthest from the center e of gravity forthe surface region including the annulus of the pulmonary and a center fof gravity for the surface region including the annulus of the tricuspidvalve, and may be extracted from its features, or may be preset.

Moreover, as illustrated in FIG. 11, a line segment connecting thecenter f of gravity for the surface region including the annulus of thetricuspid valve with the apex portion h of the right ventricle iscalculated as the second axis candidate. The annulus of the tricuspidvalve or the center f of gravity for the surface region including theannulus of the tricuspid valve may be preset, or may be extracted fromits features.

Furthermore, as illustrated in FIG. 12, a line segment connecting amiddle point g between the center f of gravity for the surface regionincluding the annulus of the tricuspid valve and the center e of gravityfor the surface region including the annulus of the pulmonary valve withthe apex portion h of the right ventricle is calculated as the thirdcandidate.

Moreover, because the right ventricle has an arch form, and an axis of acurved line along the arch form may be adopted. In such a case, asillustrated in FIG. 13, a line segment connecting a middle point gbetween the center f of gravity for the surface region including theannulus of the tricuspid valve and the center e of gravity for thesurface region including the annulus of the pulmonary valve with theapex portion h of the right ventricle is generated, and as illustratedin FIG. 14, at a middle point j of this line segment, a normal vectorv_(n) having a direction that follows the corkscrew rule in order of thepoints e, f and h is generated. Furthermore, as illustrated in FIG. 15,a straight line k passing through the normal vector v_(n) is traced toidentify a point m on a boundary surface 1 (i.e. a fluid surface of theheart muscle) that is nearest to the middle point j. Then, asillustrated in FIG. 16, a distance p between the points j and m iscalculated, and as illustrated in FIG. 17, a point q is identified,which is far away from the point j on the straight line k by apredetermined number n (n is equal to or greater than 2)*p. Finally, asillustrated in FIG. 18, a curved line smoothly connecting the points g,h and q (e.g. by a spline curve) is calculated as the axis fourthcandidate.

Then, the axis processing unit 121 outputs the axis candidates onto thedisplay unit 150 to prompt the user to select an axis to be employed(step S5). The input unit 140 accepts a selection instruction of theaxis from the user (step S7), and outputs data of the selected axis tothe vector display processing unit 120. The vector display processingunit 120 receives the data of the selected axis from the input unit 140.

Next, the plane generator 122 prompts the user to designate the numberof cross sections and a resolution of the surface region, and the inputunit 140 accepts the designation of the number of cross sections and theresolution of the surface region, and outputs data of the number ofcross sections and the resolution of the surface region to the planegenerator 122 (step S9). The plane generator 122 receives the data ofthe number of cross sections and the resolution of the surface regionfrom the input unit 140.

Then, the plane generator 122 generates Z surface regions (Z=the numberof cross sections) having the designated resolution and being orthogonalto the axis designated at the step S7, and stores data of the generatedsurface regions into the second data storage unit 130 (step S11).

For example, when the line segment connecting the center a of gravityfor the surface region including the annulus of the mitral valve withthe apex portion c is designated and the number of cross sections is “5”as illustrated in FIG. 19, 5 surface regions are generated that has apredetermined size and whose center position is at a position obtainedby equally dividing the line segment ac by “6”. Furthermore, asillustrated in FIG. 20, N*M lattice points (or grid points) (M isdesignated as the resolution.) are defined on the surface region.

Then, the vector generator 123 calculates, for each surface region, avector at each lattice point in the surface region from the vectors atvertexes of the unstructured grid (tetrahedral elements in thisembodiment), and stores calculation results into the second data storageunit 130 (step S13).

In this embodiment, as illustrated in FIG. 21, a vector at each vertexof the tetrahedral elements is defined in the first data storage unit110 for a portion that is other than the heart muscle and in which theblood flows. Therefore, for each lattice point, a tetrahedral elementencompassing this lattice point is identified to calculate a vector atthe lattice point from the vector at each vertex of the tetrahedralelement.

In other words, as illustrated in FIG. 22, a lattice point s is includedin the depicted tetrahedral element. Vectors v₁ to v₄ are defined atvertexes of this tetrahedral element. Therefore, the vector v_(s) at thelattice point s is calculated as follows:

$v_{s} = \frac{\sum\limits_{i}^{4}\; {v_{i}N_{i}}}{\sum\limits_{i}^{4}\; N_{i}}$$N_{i} = \frac{1}{d_{i}}$

“d_(i)” represents a distance between the lattice point s included inthe tetrahedral element and each vertex position i of the tetrahedralelement. Thus, the vector v_(s) at the lattice point s is a vectorobtained by linearly interpolating the vectors v₁ to v₄ at therespective vertexes.

Moreover, the vector generator 123 sets a magnitude of the vector bymultiplying a magnification, which is initially set, by magnitude of thecalculated vector (step S15).

Shifting to the processing of FIG. 23, the vector display processingunit 120 determines whether or not a relationship between the vector andthe surface region is appropriate (step S17). For example, when thevector is tangent to or penetrates a surface region different from thesurface region of a start point of the vector, it is determined that therelationship between the vector and the surface region is notappropriate. Therefore, it is determined, for each surface region,whether or the vector at each lattice point satisfies such a condition.

When the relationship between the vector and the surface region isappropriate, the rendering processing unit 124 performs rendering byusing data stored in the first data storage unit 110 for the portionsother than the heart muscle, using vector data stored in the second datastorage unit 130 for the portions in which the blood flows, anddisplaying the vectors as the arrows (step S25). Then, the processingends. As described above, when the processing is performed for pluraltime steps, the processing shifts to a processing for the next step. Inthe processing for the next step, the number of cross sections andresolution may not be changed.

On the other hand, when the relationship between the vector and thesurface region is not appropriate, the vector display processing unit120 prompts the user to input whether or not the magnitude of the vectoris changed, and the input unit 140 accepts an input concerning whetheror not the magnitude of the vector is changed. Then, when the magnitudeof the vector is changed (step S19: Yes route), the vector generator 123changes the magnitude of the vector (step S21). For example, when themagnitude of the vector may be changed by multiplying the presentmagnitude of the vector by a predetermined reduction ratio that is lessthan “1”, the predetermined ratio may be designated again by the user.Then, the processing returns to the step S17.

On the other hand, when the magnitude of the vector is not changed (stepS19: No route), the number of cross sections is changed. Therefore, theplane generator 122 performs display on the display unit 150 to promptthe user to change the number of cross sections, and the input unit 140accepts an input of the changed number of cross sections from the user(step S23). Then, the input unit 140 outputs data of the changed numberof cross sections to the plane generator 122. Then, the processingreturns to the step S11 through terminal B.

By carrying out such a processing, the arrow corresponding to the vectorcan be displayed at appropriate intervals.

For example, when a processing result of this embodiment is illustratedat the same angle as in FIG. 1, a state as illustrated in FIG. 24 isobtained. According to this figure, it becomes easy to understand howthe blood flows. Similarly, when a processing result of this embodimentis illustrated at the same angle as in FIG. 2, a state as illustrated inFIG. 25 is obtained. Also according to this figure, it becomes possibleto understand how the blood flows.

Furthermore, when the right ventricle is selected, a display asillustrated in FIG. 26 is made in the conventional art. However, whenthis embodiment is carried out as selecting the curved axis as the axis,a display as illustrated in FIG. 27 is performed. In FIG. 26, the arrowsare tangled, and it is difficult to understand the blood flow. However,in an example of FIG. 27, it becomes possible to roughly understand theblood flow.

Although the embodiments of this invention are described, this inventionis not limited to the embodiments. For example, the functional blockdiagram illustrated in FIG. 3 is a mere example, and does not alwayscorrespond to a program module configuration. Furthermore, as for theprocessing flow, various changes can be made. For example, as long asthe processing results do not change, an order of steps may be changed,and plural steps may be executed in parallel. Furthermore, a processingfor identifying an axis may be performed by various methods. In theaforementioned example, an example in which an axis is designated afterthe display target is designated was explained. However, withoutdesignating the display target, axis candidates may be presented, orafter performing a display once according to an axis that is initiallyset, the axis may be changed according to the user's designation.

Furthermore, the aforementioned processing may be executed by onecomputer or by plural computers in parallel.

In addition, the aforementioned information processing apparatus 100 isa computer devices as illustrated in FIG. 28. That is, a memory 2501(storage device), a CPU 2503 (processor), a hard disk drive (HDD) 2505,a display controller 2507 connected to a display device 2509, a drivedevice 2513 for a removable disk 2511, an input device 2515, and acommunication controller 2517 for connection with a network areconnected through a bus 2519 as illustrated in FIG. 28. An operatingsystem (OS) and an application program for carrying out the foregoingprocessing in the embodiment, are stored in the HDD 2505, and whenexecuted by the CPU 2503, they are read out from the HDD 2505 to thememory 2501. As the need arises, the CPU 2503 controls the displaycontroller 2507, the communication controller 2517, and the drive device2513, and causes them to perform predetermined operations. Moreover,intermediate processing data is stored in the memory 2501, and ifnecessary, it is stored in the HDD 2505. In this embodiment of thistechnique, the application program to realize the aforementionedfunctions is stored in the computer-readable, non-transitory removabledisk 2511 and distributed, and then it is installed into the HDD 2505from the drive device 2513. It may be installed into the HDD 2505 viathe network such as the Internet and the communication controller 2517.In the computer as stated above, the hardware such as the CPU 2503 andthe memory 2501, the OS and the application programs systematicallycooperate with each other, so that various functions as described abovein details are realized.

The aforementioned embodiments are outlined as follows:

A display processing method relating to the embodiments includes: (A)identifying an axis that is a straight or curved line inside of a space;(B) first generating plural surface regions that are orthogonal to theidentified axis; (C) second generating, from a first vector provided ateach vertex of an unstructured grid disposed inside of the space, asecond vector at each point of plural points on a surface region foreach of the generated plural surface regions, wherein the first vectorsare stored in a data storage unit; and (D) displaying an arrowcorresponding to the generated second vector.

By carrying out such a processing, vectors are represented as arrows,which are dispersed appropriately on plural surface regions that aredisposed appropriately, instead of displaying an unclear state in whichthe arrows are tangled in the space. Therefore, it becomes possible toeasily confirm the state of the fluid inside of the space.

Moreover, the aforementioned display processing method may furtherinclude: (E) determining whether or not a certain arrow corresponding tothe generated second vector intersects with another surface region or atip of the certain arrow corresponding to the generated second vector istangent to the another surface region; (F) upon determining that thecertain arrow corresponding to the generated second vector intersectswith the another surface region or the tip of the certain arrowcorresponding to the generated second vector is tangent to the anothersurface region, generating plural second surface regions that areorthogonal to the identified axis; and (G) generating, from the firstvector, a second vector at each point of plural points on each secondsurface region for each of the generated plural second surface regions.

According to this configuration, it is possible to adjust the positionsof the surface regions so as to enable the user to easily see the arrowscorresponding to the vectors.

On the other hand, the aforementioned display processing method mayfurther include: (H) determining whether or not a certain arrowcorresponding to the generated second vector intersects with anothersurface region or a tip of the certain arrow corresponding to thegenerated second vector is tangent to the another surface region; and(I) upon determining that the certain arrow corresponding to thegenerated second vector intersects with the another surface region orthe tip of the certain arrow corresponding to the generated secondvector is tangent to the another surface region, changing magnitude ofthe generated second vector.

In order to enable the user to easily see the arrows corresponding tothe vectors, the length of the arrow is shortened.

Moreover, the aforementioned identifying may include: identifying one ofat least a line segment connecting a first center of gravity for asurface region including a mitral valve (in detail, annulus thereof) ofa heart with an apex of the heart, a line segment connecting a secondcenter of gravity for a surface region including an aortic valve (indetail, annulus thereof) with the apex of the heart, a line segmentconnecting a first middle point between the first center of gravity andthe second center of gravity with the apex of the heart, a line segmentconnecting a third center of gravity for a surface region including apulmonary valve (in detail, annulus thereof) of the heart with an apexportion of a right ventricle in the heart, a line segment connecting afourth center of gravity for a surface region including a tricuspidvalve (in detail, annulus thereof) with the apex portion of the rightventricle, a line segment connecting a second middle point between thethird center of gravity and the fourth center of gravity with the apexportion of the right ventricle, and a curved line connecting the secondmiddle point with the apex portion of the right ventricle.

When the blood flow in the right ventricle or left ventricle of theheart is displayed, any of these axes is preferable.

Furthermore, the aforementioned first generating may include: generatingthe plural surface regions at positions obtained by equally dividing theidentified axis based on a designated number (in detail, by thedesignated number+1). Thus, it is possible to easily see the vectors.

Incidentally, it is possible to create a program causing a computer toexecute the aforementioned processing, and such a program is stored in acomputer readable storage medium or storage device such as a flexibledisk, CD-ROM, DVD-ROM, magneto-optic disk, a semiconductor memory, andhard disk. In addition, the intermediate processing result istemporarily stored in a storage device such as a main memory or thelike.

All examples and conditional language recited herein are intended forpedagogical purposes to aid the reader in understanding the inventionand the concepts contributed by the inventor to furthering the art, andare to be construed as being without limitation to such specificallyrecited examples and conditions, nor does the organization of suchexamples in the specification relate to a showing of the superiority andinferiority of the invention. Although the embodiments of the presentinventions have been described in detail, it should be understood thatthe various changes, substitutions, and alterations could be made heretowithout departing from the spirit and scope of the invention.

What is claimed is:
 1. A computer-readable, non-transitory storagemedium storing a program for causing a computer to execute a procedure,the procedure comprising: identifying an axis that is a straight orcurved line inside of a space; first generating plural surface regionsthat are orthogonal to the identified axis; second generating, from afirst vector provided at each vertex of an unstructured grid disposedinside of the space, a second vector at each point of plural points on asurface region for each of the generated plural surface regions; anddisplaying an arrow corresponding to the generated second vector.
 2. Thecomputer-readable, non-transitory storage medium as set forth in claim1, wherein the procedure further comprises: determining whether or not acertain arrow corresponding to the generated second vector intersectswith another surface region or a tip of the certain arrow correspondingto the generated second vector is tangent to the another surface region;upon determining that the certain arrow corresponding to the generatedsecond vector intersects with the another surface region or the tip ofthe certain arrow corresponding to the generated second vector istangent to the another surface region, generating plural second surfaceregions that are orthogonal to the identified axis; and generating, fromthe first vector, a second vector at each point of plural points on eachsecond surface region for each of the generated plural second surfaceregions.
 3. The computer-readable, non-transitory storage medium as setforth in claim 1, wherein the procedure further comprises: determiningwhether or not a certain arrow corresponding to the generated secondvector intersects with another surface region or a tip of the certainarrow corresponding to the generated second vector is tangent to theanother surface region; and upon determining that the certain arrowcorresponding to the generated second vector intersects with the anothersurface region or the tip of the certain arrow corresponding to thegenerated second vector is tangent to the another surface region,changing magnitude of the generated second vector.
 4. Thecomputer-readable, non-transitory storage medium as set forth in claim1, wherein the identifying comprises: identifying one of at least a linesegment connecting a first center of gravity for a surface regionincluding a mitral valve of a heart with an apex of the heart, a linesegment connecting a second center of gravity for a surface regionincluding an aortic valve with the apex of the heart, a line segmentconnecting a first middle point between the first center of gravity andthe second center of gravity with the apex of the heart, a line segmentconnecting a third center of gravity for a surface region including apulmonary valve of the heart with an apex portion of a right ventriclein the heart, a line segment connecting a fourth center of gravity for asurface region including a tricuspid valve with the apex portion of theright ventricle, a line segment connecting a second middle point betweenthe third center of gravity and the fourth center of gravity with theapex portion of the right ventricle, and a curved line connecting thesecond middle point with the apex portion of the right ventricle.
 5. Thecomputer-readable, non-transitory storage medium as set forth in claim1, wherein the first generating comprises: generating the plural surfaceregions at positions obtained by equally dividing the identified axisbased on a designated number.
 6. A display processing method,comprising: identifying, by using a computer, an axis that is a straightor curved line inside of a space; first generating, by using thecomputer, plural surface regions that are orthogonal to the identifiedaxis; second generating, by using the computer, from a first vectorprovided at each vertex of an unstructured grid disposed inside of thespace, a second vector at each point of plural points on a surfaceregion for each of the generated plural surface regions; and displaying,by using the computer, an arrow corresponding to the generated secondvector.
 7. A display processing apparatus, comprising: a memory; and aprocessor using the memory and configured to execute a procedure, theprocedure comprising: identifying an axis that is a straight or curvedline inside of a space; first generating plural surface regions that areorthogonal to the identified axis; second generating, from a firstvector provided at each vertex of an unstructured grid disposed insideof the space, a second vector at each point of plural points on asurface region for each of the generated plural surface regions; anddisplaying an arrow corresponding to the generated second vector.